Forecasting models for drought index using empirical wavelet transform and stochastic reconstruction approach

Abstract

Droughts are natural disasters and extreme climate events with a large impact on different areas of the economy, agriculture, water resources, tourism, and ecosystems. Hence, the ability to forecast drought is important to manage water resources for agricultural and industrial uses. Traditionally, single models have been introduced to forecast the drought data; however, single models may not be suitable to capture the nonlinear nature of the data. Therefore, this study proposed the Empirical Wavelet Transform (EWT) and Stochastic Reconstruction based on Gaussian Process Regression (GPR) and ARIMA models. The study aims to reduce the computation complexity and enhance forecasting accuracy of decomposition ensemble model by incorporating intrinsic mode functions (IMFs) reconstruction method. The proposed model comprises four steps: (i) decomposing the complex data into several IMFs using the EWT method; (ii) reconstructing the decomposed IMFs through autocorrelation into stochastic and deterministic components; (iii) forecasting every reconstructed component using GPR and ARIMA models; (iv) ensemble all forecasted components for the final output. The Standard Precipitation Index (SPI) data from Arau, Perlis; and Gua Musang, Kelantan were employed in this study for the purpose of illustration and verification. The performance of the proposed model was then compared with the following models: ARIMA, GPR, EWT-ARIMA, and EWT-GPR. Based on percentage comparisons, for the Arau region, the EWT-Stochastic Reconstruction- GPR showed improvement in accuracy with reductions of RMSE over the following models: ARIMA (11.90%), GPR (12.71%), EWT-ARIMA (8.48%), EWT-GPR (1.54%) and EWT-Stochastic Reconstruction-ARIMA (3.34%). Similarly, for the Gua Musang region, EWT- Stochastic Reconstruction-GPR yielded reductions of RMSE by around 30.40%, 32.94%, 18.87%, 4.39%, and 20.24% compared to ARIMA, GPR, EWT-ARIMA, EWT-GPR, and EWT-Stochastic Reconstruction-ARIMA models respectively. The empirical results indicated that the EWT-Stochastic Reconstruction- GPR model is the best model for forecasting drought data, followed by EWT-GP, EWT-Stochastic Reconstruction-ARIMA, EWT-ARIMA, ARIMA, and GPR models. In conclusion, the proposed method of reconstruction of IMFs based on autocorrelation enhanced the forecasting accuracy of the EWT model.